The zeros of the numerator are called the zeroes of the transfer function. The zeros of the denominator are called the poles of the transfer function. Both zeroes and poles are either real or complex conjugates.

The transfer function of a system with only complex conjugate zeroes, zi{\displaystyle z_{i}} and zi∗{\displaystyle z_{i}^{*}}, and poles pi{\displaystyle p_{i}} and pi∗{\displaystyle p_{i}^{*}}, can be written as: